• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.153-166
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• 1992

Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $\hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $\Vert \hat{T}_n - T(f) \Vert_2$ be the usual $L_2$ norm of the restriction of $\hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $\Vert \hat{T}_n - T(f) \Vert_2$ is discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.319-328
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• 2011

Let $\mathbf{c}=\{c_n\}_{n{\in}\mathbb{Z}}\in{\ell}^1(\mathbb{Z})$ and $\{f_n\}_{n{\in}\mathbb{Z}}$ be a frame (Riesz basis, respectively) of $L^2(\mathbb{R})$. We obtain necessary and sufficient conditions of $\mathbf{c}$ under which $\{\mathbf{c}{\ast}_{\lambda}f_n\}_{n{\in}\mathbb{Z}}$ becomes a frame (Riesz basis, respectively) of $L^2(\mathbb{R})$, where ${\lambda}$ > 0 and $(\mathbf{c}{\ast}_{\lambda}f)(t)\;:=\;{\sum}_{n{\in}\mathbb{Z}}c_nf(t-n{\lambda})$. When $\{\mathbf{c}{\ast}_{\lambda}f_n\}_{n{\in}\mathbb{Z}}$ becomes a frame of $L^2(\mathbb{R})$, we present its frame operator and the canonical dual frame in a simple form. Some interesting examples are included.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.113-119
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• 2010

If f is M-harmonic and integrable with respect to a weighted radial measure $\upsilon_{\alpha}$ over the unit ball $B_n$ of $\mathbb{C}^n$, then $\int_{B_n}(f\circ\psi)d\upsilon_{\alpha}=f(\psi(0))$ for every $\psi{\in}Aut(B_n)$. Equivalently f is fixed by the weighted Berezin transform; $T_{\alpha}f = f$. In this paper, we show that if a function f defined on $B_n$ satisfies $R(f\circ\phi){\in}L^{\infty}(B_n)$ for every $\phi{\in}Aut(B_n)$ and Sf = rf for some |r|=1, where S is any convex combination of the iterations of $T_{\alpha}$'s, then f is M-harmonic.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.81-87
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• 2010

In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem(BVP) $-D_0^{\alpha}+u(t)=\lambda[f(t, u(t))+q(t)]$, 0 < t < 1 u(0) = u(1) = 0, where $\lambda$ > 0 is a parameter, 1 < $\alpha$ $\leq$ 2, $D_{0+}^{\alpha}$ is the standard Riemann-Liouville differentiation, f : [0, 1] ${\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is continuous, and q(t) : (0, 1) $\rightarrow$ [0, $+\infty$] is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when $\lambda$ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.499-510
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• 2009

For a Borel function ${\psi}:\mathbb{R}{\times}\mathbb{R}{\rightarrow}\mathbb{R}$ satisfying the functional equation $\psi$ (s + t, u + v) + $\psi$(s - t, u - v) = $2\psi$(s, u) + $2\psi$(t, v), we show that it satisfies the functional equation $$\psi$$(s, t) = s(s - t)$$\psi$$(1, 0) + $$st\psi$$(1, 1) + t(t - s)$$\psi$$(0, 1). Using this, we prove the stability of the functional equation f(ax + ay, bz + bw) + f(ax - ay, bz - bw) = 2abf(x, z) + 2abf(y,w) in Banach modules over a unital $C^*$-algebra.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.367-377
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• 2024

Let G = (V, E) be a graph with p-vertices and q-edges and let R^◦ be a finite zero ring of order n. An injective function f : V (G) → {r₁, r₂, _…, r_k}, where r_i ∈ R^◦ is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R^◦ such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓_pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.

• Research in Community and Public Health Nursing
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• v.16 no.2
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• pp.137-147
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• 2005

Purpose: This study was conducted to investigate physical health status. depression. activities of daily living (ADL & IADL) of the low-income elderly who live alone in urban areas. Method: The subjects were the 400 low-income elders who live alone in Daegu city and the following instruments were used: 1. The number of self-reported physical health problems and present diseases: 2. CES-D scale for depression by Jo Nam-Oak et al. (1998): and 3. ADL scale by Katz (1989) and IADL scale by Lawton and Brody (1969). Results: 1. Visual difficulty was the most prevailing problem (55.3%) among physical problems. the second bowel elimination and the third hearing disturbance. As for present diseases. arthritis (26.5%), hypertension(24.3%) and DM (11.8%) were the most common diseases. 2. There were significant differences in physical health status according to age (t=3.115. p=.045). kind of medical security (t=-1.973. p=.049). perceived life satisfaction (F=4.966. p=.007) and the number of present diseases (F=2.937. p=.033). 3. There were significant differences in depression according to sex (t=-3.758. p=.000) . kind of medical security (t=-4.368. p=.000). perceived life satisfaction (F=35.743. p=.000) and the number of present diseases (F=4.246. p=.006). 4. There were significant differences in ADL according to sex (t=-2.136. p=.033) and age (F=4.863. p=.008). and in IADL according to sex (t=4.552, p=.000), age (F=3.090. p=.047) and kind of medical security (t=-3.306. p=.001). 5. Physical health state was correlated positively with both the number of present diseases (r=.140. p=.005) and depression (r=.352. p=.000), and negatively with ADL (r=-.176. p= .000) and IADL (r= -.230. p=.000). Depression was correlated positively with the number of present diseases (r=.169. p=.001) and negatively with both ADL (r=-.139. p=.005) and IADL (r=-.203. p= .000). Conclusion: The results of this study suggest that general characteristics are important factors for physical health status, depression. ADL and IADL of the low-income elderly who live alone and there are close relations among physical health status, the number of diseases, depression, ADL and IADL. Therefore, these results must be reflected in community health programs for the low-income elderly who live alone. In addition, this kind of study must be extended to the low-income elderly who live alone in rural areas.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Journal of the Korean Society of Safety
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• v.6 no.1
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• pp.26-30
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• 1991

Flammability, and released toxic halogen gases during combustion about two kinds of flame-retardant flexible foam(F.R. flexible PV foam) were investigated. One of the above was F.R. flexible PU foam with the containment of halogen and the other was manufactured with pure flexible PU foam in aqueous solution of alumina trihydrate(ATH) and dried 4 hours at 10$0^{\circ}C$. Flammability by L.O.I and UL94 HF-1 of the two materials were similarly shown. And combustion gases were analyzed with GC-Mass. HCI, CI$_2$ and HF were detected at both halogen being contained F.R. flexible PU foam and ATH dolng one The reason, to find halogen gases from burning ATH-containing F, R. flexible PU foam which wasn't used for any halogenated F.R., could be considered as by using trichlorofluoromethane with blowing agent to make PU foam. The relative quanity of relesed halogen gases of F.R. flexible PU foam with the containment of halogen had been indicated tree times HCI and CI$_2$, two times HF than ATH containing, respectively.

• The Journal of the Convergence on Culture Technology
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• v.6 no.2
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• pp.77-84
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• 2020

This study was to identify the relationship among self-resilience, emotion expressiveness, achievement motivation, and problem-solving ability of nursing students and provide data to increase problem-solving ability for nursing students based on the results. This research involved 229 nursing students in B city. The analyzed by the t-test, ANOVA, Pearson's correlation coefficient using SPSS/WIN 22.0. In results of the study, there were significant differences in problem-solving ability with respect to grade (F=4.021, p=.008), academic level (F=3.791, p=.024), satisfaction of major(F=11.140, p<.001), Accomplishment (F=8.000, p<.001), interpersonal relationship(F=16.944, p<.001). There were positive correlation between problem-solving ability and self-resilience(r=-.532, p<.001), between problem-solving ability and emotion expressiveness(r=.365, p<.001), between problem-solving ability and achievement motivation (r=.694, p<.001). Through this research requires the fellow study to determine the factors affecting problem-solving ability of nursing students.